A 6–foot–4, 175–pound forward, He played for coach Nat Holman at the City College of New York (CCNY) where as senior captain in 1950 led the Beavers to a 24–5 record and the NCAA basketball championship, earning MVP honors in the tournament. After the season, Dambrot was named to the Helms Athletic Foundation Basketball All-America team.

Dambrot's CCNY team also won the 1950 National Invitation Tournament (NIT), the only time that one school has won both the NCAA and NIT tournaments in the same season. Dambrot was the only senior starter on the CCNY roster that season.

A January 19, 2003, article in the New York Daily News described Dambrot as "a sharp-shooting forward known for his relentless enthusiasm."

Dambrot was selected in the first round (seventh overall) by the New York Knicks in the 1950 NBA draft, though he chose a career in dentistry after graduating from Columbia University dental school

According to a March 20, 1996, article in the New York Times by Ira Berkow, "the CCNY players who were convicted had accepted bribes from gamblers not to throw games, but to keep them under the point spreads. The players received just a few thousand dollars for their efforts, which took place during the season, but not during tournament games."

Irwin Dambrot lived his final years in Mendham, New Jersey. He died at age 81 at a hospital in Summit, New Jersey, after having suffered from Parkinson's disease for some time. He is interred at Locust Hill Cemetery in Dover, New Jersey.